2013
DOI: 10.1155/2013/906972
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Abstract: We study the existence of periodic solutions of Liénard equation with a deviating argumentx′′+f(x)x'+n2x+g(x(t-τ))=p(t),wheref,g,p:R→Rare continuous andpis2π-periodic,0≤τ<2πis a constant, andnis a positive integer. Assume that the limitslimx→±∞g(x)=g(±∞)andlimx→±∞F(x)=F(±∞)exist and are finite, whereF(x)=∫0x‍f(u)du. We prove that the given equation has at least one2π-periodic solution provided that one of the following conditions holds:2cos(nτ)[g(+∞)-g(-∞)]≠∫02π‍p(t)sin(θ+nt)dt, for allθ∈[0,2π],2ncos(nτ)[F(…

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